Partitions: Difference between revisions

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When the value of <math>\beta</math> is zero, the Whiten-Beta equation reverts to:
When the value of <math>\beta</math> is zero, the Whiten-Beta equation reverts to:


:<math>E_{oai} = C \left [ \dfrac{ \exp (\alpha) - 1}{\exp \left ( \alpha \dfrac{\bar d_i}{d_{50c}} \right ) + \exp (\alpha) - 2} \right ]</math>
:<math>E_{{\rm oa}i} = C \left [ \dfrac{ \exp (\alpha) - 1}{\exp \left ( \alpha \dfrac{\bar d_i}{d_{\rm 50c}} \right ) + \exp (\alpha) - 2} \right ]</math>


== Excel ==
== Excel ==

Latest revision as of 13:22, 2 March 2023

Description

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Model theory

Whiten-Beta

The Whiten-Beta expression for partition to overflow is:[1]

where:

  • is the index of the size interval, , is the number of size intervals
  • is the fraction of particles of size interval in the feed reporting to the overflow stream (frac)
  • is the geometric mean size of particles in size interval (mm)
  • is the corrected size at which 50% of the particle mass reports to underflow and 50% to overflow (mm)
  • is the fraction of feed liquids (or fines) split to overflow (frac)
  • is a parameter representing the sharpness of separation
  • is a term introduced to accommodate the so-called fish-hook effect, and controls the initial rise in the efficiency curve at finer sizes
  • is computed to ensure the Whiten-Beta function preserves the definition of in the presence of the fish-hook, i.e. at

The value of is not an input parameter and is computed numerically, by iteration, since by rearrangement:

When the value of is zero, the Whiten-Beta equation reverts to:

Excel

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SysCAD

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References

  1. Napier-Munn, T.J., Morrell, S., Morrison, R.D. and Kojovic, T., 1996. Mineral comminution circuits: their operation and optimisation. Julius Kruttschnitt Mineral Research Centre, Indooroopilly, QLD.